Variational Level Set Methods for Multiphase Image Segmentation on Implicit Surfaces

A variational level set model of multiphase image segmentation on implicit surfaces using level set method,intrinsic gradient and binary label functions is proposed in the paper along with its Split Bregman method.First,Chan-Vese model for two-phase image segmentation of planar piecewise constant/smooth images is extended to implicit surfaces.According to binary value labeling functions and the concept of convex relaxation,two-phase image segmentation model is transformed into a global convex optimization problem.Then the two-phase image segmentation model is extended to a multiphase variational image segmentation model on implicit surface using n-1 level set functions for n regions.The convex relaxation method is applied to the proposed variational problem of multiphase image segmentation and transforms the original problem into a sequence of convex sub-problems.To improve efficiency,every sub-optimization problem can be transformed to a problem of solving Poisson equations.Soft thresholding formulas can be employed with Split Bregman method,which introduces auxiliary variables and Bregman iterative parameters.Our experiments show that the proposed method is superior to the traditional ones in computational efficiency.